6.1 For Group 1's equations, the graph that doesn't belong is graph number 2. I looked at the equation to see if the y-intercept hit the right point on the y-axis and they all do that. Then I looked at the slope to determined if there is a point on the line if you go up a certain amount on the graph or down a certain number. Graphs 1 and 3 all follow that rule but for Graph number 2, if you go down 2 starting at 1 and then over one, it does not hit the line. This tells me that this graph is incorrect.
For Group 2's equations, the graph that doesn't belong is graph number 3. According to the equation, there are supposed to be 6 roots and there are only four roots on the graph.
For Group 3's equations, the graph that doesn't belong is graph number 1. According to the equation, there are supposed to be five roots and the graph only has three roots.
For Group 4's equation, the graph that doesn't belong is graph number 1. I looked at the other two graphs and realized that their equations do match their graphs which means that graph 1 is was the incorrect one.
If the leading co-efficient of an equation is positive, this means that as you move to the right on the x-axis, y goes to positive infinity. If the leading co-efficient is negative, then the y on the right side will go to negative infinity. If then equation has an odd degree, then y on the left side will go to negative infinity. However, if the equation has an even degree, then as you move to the left on the x-axis, y will go to positive infinity.
6.2
In class, we have learned the rules of exponents when solving equations. When multiplying variables together, you have to break it down each time there is a new number or variable. If it says x squared, you would write it out as x times x. Then you add it all together and combine it to get one final answer. To divide variables, you first have to find the factors of the number that is the one dividing. So if it's 6, you could say 2 times 3. And if it is cubed, it would be 2 times 3 times x times x times x. You put the number that you are dividing by on the bottom and break it down like you would for multiplying variables. Combine the remaining numbers and variables and that will give you your final answer. We also learned how to add and subtract terms of the same variable and exponent. The variables must have the same base and the same exponent to be able to add and subtract the terms. If you are sure that the base and the exponent are the same, you can just carry out regular subtraction to find your answer. Like I said, you can not add or subtract terms of different variables or different exponents. You can use this knowledge to solve problems like f(x) + g(x). We also learned about polynomial long division and synthetic division. Look at the equation and write down all the leading co-efficients. Then write the number outside the division box that is a factor of the final number of the equation. Bring the first leading co-effiecient down and then multiply the number outside the division box by that number and write the product under the second leading co-efficient. Continue multiplying the number outside the division box by the numbers on the bottom and adding and subtracting them. Stop once you get a root or a point. If it is a point, you need to keep plugging in numbers outside the division box to try and find the correct amount of roots. If you find one roots, look at the equation to determine how many roots you need and keep doing synthetic division. 6.3 On the worksheet.
6.4
Overall, I have had a good year in Algebra 2 CP. I pretty much always complete my homework assignments and always do the work given to us in class. If I don't understand something, I try to ask my classmates for help. Since it is towards the end of the school year, my goal is to not get lazy and continue doing all my work. My grades are very good in this class and I would like to continue getting an A, but maybe one closer to the A+ area, like a 95.
6.5
On the handout
6.6
k(x) = (x+3)(x+1)(x+5) and i(x) = x^4+x^3-7x^2-x+6 match graph 2 because the graph has x-intercepts of -3, -1, and -5 and it has a y-intercept of 6.
m(x) = -(x+3)(x+1)(x+5) and l(x) = -x^4-x^3+7x^2+x-6 match graph 3 because the graph has x-intercepts of -3, -1, and -5 and it has a y-intercept of 6.
q(x) = -(x+2)(x-2)(x-1)(x-5) and u(x) = -x^4+6x^3-x^2-24x+20 match graph 6 because the graph has x-intercepts of -2, 2, 1, and 5 and it has a y-intercept of 20.
z(x) = x^3+7x^2-4x-28 matches graph 1 because it has a y-intercept of -28.
p(x) = -(x+1)(x-1)(x+3)(x-2) matches graph 5 because those are the roots it has on the graph and also the leading co-efficient is negative which means the right side goes down and it does.
I first looked at the equations with the 3 x-intercepts because I thought it would be easier to find which graph matched up with it. I looked to see if the leading co-efficient was negative or positive because that would tell me which direction the right side was going in. I also looked at the y-intercepts of the equations to see what point on the graph the y-axis hit. The second group of equations was harder to match because it didn't give you the roots and you only had the y-intercept and the number of roots to look for. I narrowed down the choices by looking at the equations and finding out how many roots I needed, if the leading co-efficient was negative or positive, and what the y-intercept was.
6.7
1. For the first equation, the domain is (-infinity, +infinity). For the second equation, the domain is (-infinity, +infinity). The lines keep going so you can't tell where they stop, therefore they go to infinity.
2. For the first equation, the range is [71, -infinity). For the second equation, the range is (-10, +positive infinity.) You can see where it stops one time but then the two lines split and go to infinity.
3. B(7) = 47 and G(9) = 51. This means that when the age of boys is 7, the average height is 47 inches. It also means that when the age of girls is 9, the average heigh is 51 inches.
4. The average height of boys is greatest at age 18.
For Group 1's equations, the graph that doesn't belong is graph number 2. I looked at the equation to see if the y-intercept hit the right point on the y-axis and they all do that. Then I looked at the slope to determined if there is a point on the
line if you go up a certain amount on the graph or down a certain number. Graphs 1 and 3 all follow that rule but for Graph number 2, if you go down 2 starting at 1 and then over one, it does not hit the line. This tells me that this graph is incorrect.
For Group 2's equations, the graph that doesn't belong is graph number 3. According to the equation, there are supposed to be 6 roots and there are only four roots on the graph.
For Group 3's equations, the graph that doesn't belong is graph number 1. According to the equation, there are supposed to be five roots and the graph only has three roots.
For Group 4's equation, the graph that doesn't belong is graph number 1. I looked at the other two graphs and realized that their equations do match their graphs which means that graph 1 is was the incorrect one.
If the leading co-efficient of an equation is positive, this means that as you move to the right on the x-axis, y goes to positive infinity. If the leading co-efficient is negative, then the y on the right side will go to negative infinity. If then equation has an odd degree, then y on the left side will go to negative infinity. However, if the equation has an even degree, then as you move to the left on the x-axis, y will go to positive infinity.
6.2
In class, we have learned the rules of exponents when solving equations. When multiplying variables together, you have to break it down each time there is a new number or variable. If it says x squared, you would write it out as x times x. Then you add it all together and combine it to get one final answer. To divide variables, you first have to find the factors of the number that is the one dividing. So if it's 6, you could say 2 times 3. And if it is cubed, it would be 2 times 3 times x times x times x. You put the number that you are dividing by on the bottom and break it down like you would for multiplying variables. Combine the remaining numbers and variables and that will give you your final answer. We also learned how to add and subtract terms of the same variable and exponent. The variables must have the same base and the same exponent to be able to add and subtract the terms. If you are sure that the base and the exponent are the same, you can just carry out regular subtraction to find your answer. Like I said, you can not add or subtract terms of different variables or different exponents. You can use this knowledge to solve problems like f(x) + g(x). We also learned about polynomial long division and synthetic division. Look at the equation and write down all the leading co-efficients. Then write the number outside the division box that is a factor of the final number of the equation. Bring the first leading co-effiecient down and then multiply the number outside the division box by that number and write the product under the second leading co-efficient. Continue multiplying the number outside the division box by the numbers on the bottom and adding and subtracting them. Stop once you get a root or a point. If it is a point, you need to keep plugging in numbers outside the division box to try and find the correct amount of roots. If you find one roots, look at the equation to determine how many roots you need and keep doing synthetic division.
6.3
On the worksheet.
6.4
Overall, I have had a good year in Algebra 2 CP. I pretty much always complete my homework assignments and always do the work given to us in class. If I don't understand something, I try to ask my classmates for help. Since it is towards the end of the school year, my goal is to not get lazy and continue doing all my work. My grades are very good in this class and I would like to continue getting an A, but maybe one closer to the A+ area, like a 95.
6.5
On the handout
6.6
k(x) = (x+3)(x+1)(x+5) and i(x) = x^4+x^3-7x^2-x+6 match graph 2 because the graph has x-intercepts of -3, -1, and -5 and it has a y-intercept of 6.
m(x) = -(x+3)(x+1)(x+5) and l(x) = -x^4-x^3+7x^2+x-6 match graph 3 because the graph has x-intercepts of -3, -1, and -5 and it has a y-intercept of 6.
q(x) = -(x+2)(x-2)(x-1)(x-5) and u(x) = -x^4+6x^3-x^2-24x+20 match graph 6 because the graph has x-intercepts of -2, 2, 1, and 5 and it has a y-intercept of 20.
z(x) = x^3+7x^2-4x-28 matches graph 1 because it has a y-intercept of -28.
p(x) = -(x+1)(x-1)(x+3)(x-2) matches graph 5 because those are the roots it has on the graph and also the leading co-efficient is negative which means the right side goes down and it does.
I first looked at the equations with the 3 x-intercepts because I thought it would be easier to find which graph matched up with it. I looked to see if the leading co-efficient was negative or positive because that would tell me which direction the right side was going in. I also looked at the y-intercepts of the equations to see what point on the graph the y-axis hit. The second group of equations was harder to match because it didn't give you the roots and you only had the y-intercept and the number of roots to look for. I narrowed down the choices by looking at the equations and finding out how many roots I needed, if the leading co-efficient was negative or positive, and what the y-intercept was.
6.7
1. For the first equation, the domain is (-infinity, +infinity). For the second equation, the domain is (-infinity, +infinity). The lines keep going so you can't tell where they stop, therefore they go to infinity.
2. For the first equation, the range is [71, -infinity). For the second equation, the range is (-10, +positive infinity.) You can see where it stops one time but then the two lines split and go to infinity.
3. B(7) = 47 and G(9) = 51. This means that when the age of boys is 7, the average height is 47 inches. It also means that when the age of girls is 9, the average heigh is 51 inches.
4. The average height of boys is greatest at age 18.